Mathematical Characteristics of Uplink and Downlink Interference Regions in D2D Communications Underlaying Cellular Networks

In this paper, mathematical characteristics of uplink and downlink interference regions in device-to-device (D2D) communications underlaying cellular networks are analyzed. We consider that one CUE and one pair of D2D user equipments (DUEs) coexist and share uplink and downlink resources of cellular networks. The DUE pair consists of a D2D transmitting user equipment and a D2D receiving user equipment. Therefore, additional interference between the CUE and the DUE pair is introduced. First, uplink and downlink interference regions are defined and described. Next, mathematical characteristics of uplink and downlink interference regions are derived. Finally, blocking probability is formulated based on the mathematical characteristics values. The analysis results show that uplink resources are more suitable to be shared for the CUE and the DUE pair, but the difference between uplink and downlink is not significant. Meanwhile, the simulation results show that theoretical values of blocking probability well match simulation results. The results can provide a theoretical foundation for resource allocation and optimization of D2D communications.